ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60 Mishura, Yuliya, Kiev University, Ukraine Generalized stochastic integrals with application to fractional Brownian motion The generalized stochastic integral of the first and higher orders up to the square-integrable processes is constructed. The integration up to the Wiener process, square-integrable martingales, Gaussian processes, especially fractional Brownian motion (FBM) with Hurst index 0 < H < 1, is presented as particular case. Nontraditional Ito formula containing [1/H] generalized stochastic integrals of higher order, Dolean exponent and Dolean equation for FBM are deduced. Stochastic differential equations containing stochastic integrals up to FBM with 0 < H < 1/2 are investigated. Girsanov theorem for FBM with 1/2 ≤ H < 1 and with “stochastic drift” is proved.